The role of the intergranular and intragranular critical current densities in silver-sheathed Pb-Bi-Sr-Ca-Cu-O tapes is investigated by means of magnetic-moment measurements in perpendicular field at different temperatures using a superconducting quantum interference device magnetometer. We find that low-field magnetic-moment loops are mainly caused by the intergranular (transport) critical current density JcJ but that in high fields the contribution from the intragranular critical current density JcG becomes significant. The low-field data can be described well in terms of a critical-state model for a thin strip of a homogeneous type-II superconductor in a perpendicular field where JcJ flows over the entire tape. The high-field data require in addition a description in terms of a critical-state model for the grains where JcG circulates in each grain. Strong mechanical bending of the tape causes JcJ to disappear while JcG is unaffected. The experimental data reveal the hysteretic nature of JcJ which is caused by the trapping of flux in grains. In all the tapes measured, JcJ is found to be much smaller than JcG. Comparing the remanent JcJ with JcG in different tapes, we find that strong pinning in grains does not imply a high remanent intergranular critical current density.